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Lec 93 - Alternate Proof to Induction for Integer Sum

Alternate Proof to Induction for Integer Sum Another way to prove the expression for the sum of all positive integers up to and including n

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Lecture list for this course

Lec 1 - The Beauty of Algebra

Lec 2 - Origins of Algebra

Lec 3 - Abstract-ness

Lec 4 - Descartes and Cartesian Coordinates

Lec 5 - Variables Expressions and Equations

Lec 6 - Simple Equations

Lec 7 - Equations 2

Lec 8 - Equations 3

Lec 9 - Algebra: Linear Equations 4

Lec 10 - Algebra: Solving Inequalities

Lec 11 - Algebra: graphing lines 1

Lec 12 - Algebra: Slope and Y-intercept intuition

Lec 13 - Algebra: Slope

Lec 14 - Algebra: Slope 2

Lec 15 - Algebra: Slope 3

Lec 16 - Algebra: Equation of a line

Lec 17 - Slope and Y-intercept Intuition

Lec 18 - Averages

Lec 19 - Integer sums

Lec 20 - Taking percentages

Lec 21 - Growing by a percentage

Lec 22 - Another Percent Word Problem

Lec 23 - More percent problems

Lec 24 - systems of equations

Lec 25 - Introduction to Ratios (new HD version)

Lec 26 - Ratio problem with basic algebra (new HD)

Lec 27 - More advanced ratio problem--with Algebra (HD version)

Lec 28 - Alternate Solution to Ratio Problem (HD Version)

Lec 29 - Introduction to Ratios

Lec 30 - Advanced ratio problems

Lec 31 - Age word problems 1

Lec 32 - Age word problems 2

Lec 33 - Age word problems 3

Lec 34 - Level 1 multiplying expressions

Lec 35 - Solving a quadratic by factoring

Lec 36 - Introduction to i and Imaginary Numbers

Lec 37 - Calculating i Raised to Arbitrary Exponents

Lec 38 - i as the Principal Root of -1 (a little technical)

Lec 39 - Complex Numbers (part 1)

Lec 40 - Complex Numbers (part 2)

Lec 41 - Introduction to the quadratic equation

Lec 42 - Quadratic Equation part 2

Lec 43 - Completing the square

Lec 44 - Quadratic Formula (proof)

Lec 45 - Quadratic Inequalities

Lec 46 - Quadratic Inequalities (Visual Explanation)

Lec 47 - Introduction to functions

Lec 48 - Functions Part 2

Lec 49 - Functions (Part III)

Lec 50 - Functions (part 4)

Lec 51 - Domain of a function

Lec 52 - Proof: log a + log b = log ab

Lec 53 - Proof: A(log B) = log (B^A), log A - log B = log (A/B)

Lec 54 - Proof: log_a (B) = (log_x (B))/(log_x (A))

Lec 55 - Algebraic Long Division

Lec 56 - Introduction to Conic Sections

Lec 57 - Conic Sections: Intro to Circles

Lec 58 - Conic Sections: Intro to Ellipses

Lec 59 - Conic Sections: Intro to Hyperbolas

Lec 60 - Conic Sections: Hyperbolas 2

Lec 61 - Conic Sections: Hyperbolas 3

Lec 62 - Identifying Conics 1

Lec 63 - Identifying Conics 2

Lec 64 - Conic Identification 3

Lec 65 - Foci of an Ellipse

Lec 66 - Foci of a Hyperbola

Lec 67 - Proof: Hyperbola Foci

Lec 68 - Partial Fraction Expansion 1

Lec 69 - Partial Fraction Expansion 2

Lec 70 - Partial Fraction Expansion 3

Lec 71 - Parabola Focus and Directrix 1

Lec 72 - Focus and Directrix of a Parabola 2

Lec 73 - Two Passing Bicycles Word Problem

Lec 74 - Passed Bike Word Problem

Lec 75 - Passing Trains

Lec 76 - Overtaking Word Problem

Lec 77 - Early Train Word Problem

Lec 78 - Officer on Horseback

Lec 79 - Rational Inequalities

Lec 80 - Rational Inequalities 2

Lec 81 - Interesting Polynomial Coefficient Problem

Lec 82 - Geometric series sum to figure out mortgage payments

Lec 83 - Introduction to Function Inverses

Lec 84 - Function Inverse Example 1

Lec 85 - Function Inverses Example 2

Lec 86 - Function Inverses Example 3

Lec 87 - Direct and Inverse Variation

Lec 88 - Recognizing Direct and Inverse Variation

Lec 89 - Recognizing Odd and Even Functions

Lec 90 - Connection between even and odd numbers and functions

Lec 91 - New Operator Definitions

Lec 92 - Proof by Induction

Lec 94 - Writing Proportions

Lec 95 - Coverting Repeating Decimals to Fractions 1

Lec 96 - Coverting Repeating Decimals to Fractions 2